I have a question about limits of piecewise defined functions. Given two piecewise functions, f(x) and g(x), who's limits don't exist at x = 2, is it possible for the limit x->2 (f(x) + g(x)) to exist? I have had two AP summer institutes who's instructors showed that this is possible by looking at the left and right limits. I am now looking at the newest Anton, Bivens, Davis (Calculus ET 10th edition) solutions and they show such a problem where the solution says the limit DNE because one of the function's limits DNE. It is true that the final answer is DNE by looking at the left and right limits, but this is not the reason given in the solutions on line. Any insight would help. Thanks.